Question

(a) Evaluate: L (2+5x)e 'dx 9Marks (b) Determine the area enclosed between the curves y = x + 1 and y = 7-X 8Marks (C) Water is leaking from a pipe and the volume. V litres, of the water is decreasing at the rate (6-21) litres per minutes after t minutes. Assuming that V = 9 when t = 0, find V in terms of t. 7 Marks (d) Find the equation of the curve that passes through (26) If the stope of the curve is given by x = 3x at any point X. 7Marks (e) The marginal cost of producing x units of a commodity is given by C(x) = 0.3x + 2x, and the fixed cost is GHC 2000.00, find the cost function C(x) and the cost of producing 20 units. 9Marks

Answer 1

6 6 5*2*5m) -- : 1,966 vas-te provede (22+5). Se $3,7° F45,(045)/ Land - (245x).edu ( 0 [ Integrating by posts] 11 {$(245). e)* (*.3.cºm) 24 da 2 960 +6 11 6 17 + 15% -96e2+6 + 15x3[es]. - 96e2+6 + 45 e?45 51e²-39 (51 e?+39) (-3,10) (Reed) 13 11 - 11 (797-) y=7-X y=xl te (155) de b) Y=557,6255) 699 4 & (6) J = x²+1 y = 7-2 Cr-cü 22+1 =70 => 42+71-6=0 B+3)(x-2)=0 25-3,2 When x=-3, ("> y=10 =) (26%) = (-3,10) When x=2, (u) y = 5 = (xgy). (1) & (u meet two pts (-3,10) and # Throeg P, a lone Il to x-axis drawn to meet again at (-2,5) = (2,5) (2,5) at region PoQP area of PNPIQP Area of the shaded Area of POPNO + 2 x( Area of Pon) + Area of PNPIQP

2 = 2x + 2 2 2-030. J (1-1)-12.vie . (1-x2) dx + *.5-2) da (52-5°) 2 [2 - ] - 2 2 2 3 + 11 2 [ 2 0 + 20 56 unit. (Regd.) - squatte c) Condition the problem, of By the dy de - (6-2t) dy -(6-24)dt dy: - / (6-22) at [ c = Int. const.) + G -(6t+t2) V = ,0 % V:9 at Initially C 9 = (Regd.) (1) 8 új → y = 9-6tr 42 d ) dy C- In Constanta - 342 dy : 322 da Jay = 3/22 dx y2 슬 등 3y2 = 2n3tc When it possess through (2,6) then (1) + 3×36 = 2x8+c 23 + >C= 92 2 .05 13y2– 2x3 +92 is the req&. curve.

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